n cards are laid on a table, all face down. The 1st person selects 1 card at random and turns it over, the 2nd person selects 2 cards at random and turns them over, the 3rd person selects 3 cards at random and turns them over, and so on, until the nth person turns all the n cards over.

Determine all n such that it is possible for all n cards to be face up at the end.

Maybe the person who thinks they have the correct answer doesn't have the correct answer. It seems pretty straightforward to me - if the solution is something else then the problem is semantics, not math.